The aim of this course is to provide participants with a fast track to frontier research of great contemporary interest starting from the revisiting of foundational aspects of the Mechanics of Solids and Structures. The course primarily targets beginning graduate students and young researchers who want to get an accelerated introduction to recent progress in the analysis of the response and failure of advanced materials and active systems, including biological ones.
A. De Simone and P. Reis will lecture on the mechanics of slender structures (rods, plates and shells), both active and passive, and applications to adaptive structures and to soft and bioinspired robotics. L. De Lorenzis and K. Ravi-Chandar will lecture on Fracture Mechanics, from modern experimental and theoretical foundations to recent advances on phase-field modeling and computation, and applications to biological tissues and porous media.
A. Goriely and Ellen Kuhl will lecture on the mechanobiology of growth and morphogenesis, and applications to quantitative modeling of the human brain.
The detailed plan of the lectures is the following.
Mechanics of 2d rods from Euler’s elastica to robotic arms and elephant trunks (ADS)
Kinematics and equilibrium of active planar rods in the large deformation regime; variational methods: the principle of virtual power and the finite element method.
Applications 1: shape control of structural systems with cables and tendons;
applications 2: shape control through active bending (snakes and elephant trunks);
applications 3: spontaneous oscillations in biological filaments and growing plant shoots.
Mechanics of 3d rods, plates and shells (PR)
Mechanics of rods – Kirchhoff’s rod theory: Kinematics & Equilibrium. Examples and Applications; Plates I: Pure bending deformation. Wrinkling; Plates II: Föppl-von Kárman (nonlinear) theory of plates. Plate buckling; Shells I: Linear pressure vessels, A primer on differential geometry, Dimensional reduction (3D-2D). Linear shell theory; Shells II: Nonlinear DMV shell theory. Shell buckling; Magneto-active Rods, Plates, and Shells.
Fracture Mechanics (KRC)
Griffith theory of fracture – the global approach; Engineering fracture mechanics – the local approach; Experimental fracture mechanics; Mixed-mode fracture – crack path selection; Elastic plastic fracture; Dynamic fracture.
Variational phase-field modeling of fracture (LDL)
The variational approach to brittle fracture; the phase-field regularization: main modeling components; crack nucleation vs. propagation, energy decomposition; computational aspects; phase-field modeling of ductile fracture; applications to anisotropic tissues and porous media.
The mathematics and mechanics of biological growth (AG)
The problem of growth; Growing in 1D: rods and filaments; Growing in 2D: membranes, plates, and shells; Growing in 3D: nonlinear elasticity and theory; Growing in 3D: applications (plants, arteries, and the brain); From 3D to 1D: dimensional reduction with applications.
Integrating mechanics and computation to understand the human brain (EK)
Introduction to Neuromechanics; Elasticity of the brain - Characterizing brain stiffness dead and alive; Growth of the brain; Understanding neurodevelopment; Damage of the brain - Traumatic brain injury and neurodegeneration; Machine learning and the brain; Integrating neuroimaging and mechanics.- Automated model discovery - Learning models for human brain.